For the curve f(x) = x3, x = 0 is

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45th BPSC Prelims (Held in 2002) Official paper
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  1. the global minimum point
  2. the local minimum point
  3. an extreme point
  4. a point of inflexion

Answer (Detailed Solution Below)

Option 4 : a point of inflexion
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Detailed Solution

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The correct answer is option 4.

Given:  the curve f(x) = x3

Calculation:

⇒ f(x) = x3

For the value of x = 0, f(0) = 03 = 0

For x = 2 , f(2) = 23 = 8

For x = -2, f(-2) = (-2)3 = -8;

So, x = 0 will be a point of inflexion for the given cubic function.

Additional Information

  •  Inflexion points are points where the function changes concavity, i.e. from being "concave up" to being "concave down" or vice versa.

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